What is the d/(dz)(z/(z+a/z)) ?

The d/(dz)(z/(z+a/z)) is (2az)/((z^2+a)^2)

What is the first d/(dz)(z/(z+a/z)) ?

The first d/(dz)(z/(z+a/z)) is (2az)/((z^2+a)^2)

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\frac{d}{d z} (\frac{z}{z + \frac{a}{z}})

\frac{2 a z}{( z ^{2} + a ) ^{2}}

Solution steps

\frac{d}{d z} (\frac{z}{z + \frac{a}{z}})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d z}{d z} ( z + \frac{a}{z} ) - \frac{d}{d z} ( z + \frac{a}{z} ) z}{( z + \frac{a}{z} ) ^{2}}

\frac{d z}{d z} = 1

\frac{d}{d z} (z + \frac{a}{z}) = 1 - \frac{a}{z ^{2}}

= \frac{1 \cdot ( z + \frac{a}{z} ) - ( 1 - \frac{a}{z ^{2}} ) z}{( z + \frac{a}{z} ) ^{2}}

Simplify

\frac{1 \cdot ( z + \frac{a}{z} ) - ( 1 - \frac{a}{z ^{2}} ) z}{( z + \frac{a}{z} ) ^{2}} : \frac{2 a z}{( z ^{2} + a ) ^{2}}

= \frac{2 a z}{( z ^{2} + a ) ^{2}}

y^{^{''}} + 2 y^{^{'}} = 8 x

(2 x + 1) \frac{d y}{d x} = 4 x y

\int \frac{sec ( x ) + cos ( x )}{3 cos ( x )} d x

\frac{x}{x ^{2} + 3}

\int cos^{2} (x s i) n^{3} x d x

What is the d/(dz)(z/(z+a/z)) ?
The d/(dz)(z/(z+a/z)) is (2az)/((z^2+a)^2)
What is the first d/(dz)(z/(z+a/z)) ?
The first d/(dz)(z/(z+a/z)) is (2az)/((z^2+a)^2)